Kamara, the game's most impressive performer, struck seven minutes into the second half after Millwall had taken a first-half lead.
Both sides stated their attacking intentions from the first whistle with early chances created at both ends.
Danny Spiller brought a fine reaction save out of Terriers keeper Matthew Glennon in only the second minute, while Huddersfield's goal-machine Luke Beckett shot straight at Chris Day when well placed in the area.
Millwall's midfield slowly began to assume control as the game settled down, but they were unable to convert a series of chances, much to the frustration of the home crowd.
After Gary Alexander missed a gilt-edged chance, the breakthrough finally came in the 41st minute when full-back Danny Senda picked out Paul Robinson with a delightful chip to the far post and the captain guided a firm header past Glennon's despairing dive.
The Lions had barely finished celebrating when Town's debutant defender Richard Keogh struck a raking crossfield pass straight onto the head of Andy Booth, whose looping header caught Day in no-man's land and found the net for the equaliser.
Town seized the initiative from the start of the second half and went in front on 53 minutes. The impressive Kamara dazzled the Millwall defence with some neat skill in the area before calmly placing the ball past Day.
Kamara continued to pose problems with his pace and trickery as the Lions struggled to find an equaliser.
They almost snatched one in the final minute, but substitute Jay Simpson's volley flashed agonisingly wide of Glennon's left-hand post.